Summarizing Numerical Data

Student Survey

Lock5withR includes a data set with data from a student survey. It includes the following variables.

• Year Year in school
• Gender Student’s gender: ‘F’ or ‘M’
• Smoke Smoker? ‘No’ or ‘Yes’
• Award Prefered award: ‘Academy’ ‘Nobel’ ‘Olympic’
• HigherSAT Which SAT is higher? ‘Math’ or ‘Verbal’
• Exercise Hours of exercsie per week
• TV Hours of TV viewing per week
• Height Height (in inches)
• Weight Weight (in pounds)
• Siblings Number of siblings
• BirthOrder Birth order, 1=oldest
• VerbalSAT Verbal SAT score
• MathSAT Math SAT score
• SAT Combined Verbal + Math SAT
• GPA College grade point average
• Pulse Pulse rate (beats per minute)
• Piercings Number of body piercings

names(StudentSurvey)

##  [1] "Year"       "Gender"     "Smoke"      "Award"      "HigherSAT" 
##  [6] "Exercise"   "TV"         "Height"     "Weight"     "Siblings"  
## [11] "BirthOrder" "VerbalSAT"  "MathSAT"    "SAT"        "GPA"       
## [16] "Pulse"      "Piercings"  "Sex"

nrow(StudentSurvey)

## [1] 362

Question: Which variables are categorical, which quantitative?

Exercise

Let’s take a look at one of the variables: Exercise. Here are some histograms of the Exercise variable.

gf_histogram( ~ Exercise, data = StudentSurvey, binwidth = 1, alpha = 0.5)
gf_histogram( ~ Exercise, data = StudentSurvey, binwidth = 3, alpha = 0.5)
gf_histogram( ~ Exercise, data = StudentSurvey, binwidth = 5, alpha = 0.5)

1. Which binwidth do you like best? Why?

2. What does the tallest bar in the histogram with binwidth 5 represent?
   (Be as specific as you can given the resolution of the plot.)

3. Why is there a gap with no bars near the right end of the graph? What does that represent?

4. How would you describe the shape of the histogram(s)?

5. Use the histograms to estimate the mean and the median. Which one should be larger? Why? A lot larger or just a little larger? Now compute the mean and median and see if you are right.

6. Sketch what you think a boxplot for this data set looks like. Then create one and see how your sketch compares.

7. Use your boxplot to estimate the IQR. Then compute the IQR to see how close your estimate is.

8. An alternative to a histogram is called a frequency polygon.

   1. Look at the example below and describe in words how a frequency polygon compares to a histogram?
   2. Why might someone prefer a frequency polygon to a histogram?

gf_histogram( ~ Exercise, data = StudentSurvey, alpha = 0.5, binwidth = 5) %>%
 gf_freqpoly( ~ Exercise, data = StudentSurvey, binwidth = 5)

8. This plots below are “smooth versions” of a histogram. What the advantages and disadvantages of these density plots vs. histograms?

gf_dhistogram( ~ Exercise, data = StudentSurvey, alpha = 0.5) %>% 
gf_density( ~ Exercise, data = StudentSurvey)
gf_density( ~ Exercise, data = StudentSurvey, adjust = 2)  # twice as smooth
gf_dens( ~ Exercise, data = StudentSurvey, adjust = 0.5)   # half as smooth (& "open")

9. How would you expect the shape to change if you made a histogram for log(Exercise)? Try it and see if you are right. What happens if you use log10() instead of log()? [log() is natural log and log10() is log base 10. You can also use log2() for log base 2.]

10. Create several plots to compare Exercise for men and women. Describe what your plots tell you.

11. Create several plots to compare Exercise for students in different academic years. Describe what your plots tell you.

Finished? Try looking at some other quantitative variables, like Piercings or Pulse. Make some plots and see what they tell you about these variables.